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April, 1975 On the Distribution of the Maximum of the Sequence of Sums of Independent Random Variables
T. Gergley, I. I. Yezhow
Ann. Probab. 3(2): 289-297 (April, 1975). DOI: 10.1214/aop/1176996399

Abstract

Let $\xi_1, \xi_2, \cdots$ be independent random variables. The distribution of $\max (0, \xi_1, \xi_1 + \xi_2, \cdots, \xi_1 + \cdots + \xi_n)$ is investigated by means of a method based on the construction of certain events with easily determined proabilities. These yield a new formula for the distribution of the maximum which is sometimes more useful than that given in literature.

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T. Gergley. I. I. Yezhow. "On the Distribution of the Maximum of the Sequence of Sums of Independent Random Variables." Ann. Probab. 3 (2) 289 - 297, April, 1975. https://doi.org/10.1214/aop/1176996399

Information

Published: April, 1975
First available in Project Euclid: 19 April 2007

MathSciNet: MR372993
Digital Object Identifier: 10.1214/aop/1176996399

Subjects:
Primary: 60G50
Secondary: 60F99 , 60I15

Keywords: Maximum distribution of , Random walk , Sums of independent random variables

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 2 • April, 1975
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